# Эксперимент: Wick-Matching Polynomial Interaction Layer (#1196)

{
  "worked": false,
  "confidence": 8,
  "verdict": "Built an exact degree-3 Wick-matching layer with enumerated perfect-match coefficients, PSD matrix construction, and trace-power features. The core identity matched 30,000-sample Gaussian Monte Carlo within 0.29%, confirming the combinatorial expansion. Wick regression had lower RMSE (6.12 vs 8.10), but used substantially more parameters (4,623 vs 1,761), so this is not evidence of a win at comparable parameter count.",
  "metrics": {
    "baseline": "DeepSets: test RMSE 8.1012, 1,761 parameters, permutation output difference 9.54e-7",
    "idea": "Wick layer: test RMSE 6.1223, 4,623 parameters, permutation output difference 6.59e-5; exact-vs-Monte-Carlo maximum relative error 0.00289"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 wick_experiment.py",
  "files": [
    "wick_experiment.py",
    "results_equal_params.json"
  ],
  "limitations": "Only a small synthetic degree-3 regression task was tested; no QM9 or graph benchmark, FLOP-matched comparison, unconstrained bilinear control, repeated seeds, gradient-variance analysis, orthogonal-transformation test, or running-statistics normalization was evaluated. The regression improvement is confounded by substantially higher parameter count."
}